Adopting a Bayesian perspective, [1]} determines the smallest convex ambiguity sets that contain the unknown data-generating distribution with a prescribed level of confidence as the sample size increases. Both the Pearson divergence and relative entropy ambiguity sets with properly scaled radii are optimal in this setting. [1]} however restricts attention to the subclass of distributionally robust predictors with convex ambiguity sets whereas here a much richer class of predictors is considered. [3]} also seeks distributionally robust predictors which trade conservatism for out-of-sample performance. [3]} studies in particular the probability that the estimated expected cost function dominates the actual expected cost function uniformly across all decisions, and he calls a predictor optimal if this probability is asymptotically equal to a prescribed confidence level. Using the empirical likelihood theorem of [5]}, he shows that Pearson divergence and relative entropy ambiguity sets with properly scaled radii are optimal in this sense.
